Basically, it's a PSPACE reduction. In more depth, it proves an upper bound for the complexity of this one computer security model my prof created. I had to turn it into a graph problem and then... oh, it's just a big mess. I'm proud of this one because it got me Erdos 4.

Ahw, these all look mighty interesting, but as usual I'm having a hard(er) time to understand because it is in english.

Drat.

And I'm not going to bother to upload my paper about the mathematics behind depth perception and how to calculate dimensions of a 3d object from a perspective view from 1 plane (My specialisation in maths was (tri)geometry) or 2 planes.
Because it is in dutch.

Basically, it's a PSPACE reduction. In more depth, it proves an upper bound for the complexity of this one computer security model my prof created. I had to turn it into a graph problem and then... oh, it's just a big mess. I'm proud of this one because it got me Erdos 4.

Basically, it's a PSPACE reduction. In more depth, it proves an upper bound for the complexity of this one computer security model my prof created. I had to turn it into a graph problem and then... oh, it's just a big mess. I'm proud of this one because it got me Erdos 4.

I'll be Erdos 4 in (hopefully) another couple months.

Yeah, the only Erdos numbers that really count are 1 and 0. Otherwise, it basically just means you got a joint paper with someone reputable published (usually your adviser ).

This might be a little more comprehensible, as it doesn't assume too much prior knowledge. On the other hand, it's a lot of details.

Interesting stuff!

This might be the wrong thread to mention it, but your paper made me start thinking about words with more possible digits, so I played around with some ternary "path bundles" (obviously the definition had to be modified). It seems that analogues Lemma 1 and Lemma 2 hold for all p-ary path bundles (p a natural number), but I haven't tried it for higher p yet, and I certainly haven't proved the existence theorems!

Let a "path" be as before, but require that adjacent words differ only in one digit AND only by 1, with no wrap-around. So in base p=5, you have 0142~0132, but NOT 0142~0102.

Now specify that B(n,a,p) has p^a paths, and for each w in Qa whose digits include only 0 and p-1 (i.e. the true "vertices" of Qa), the bundle contains Pw such that
1. |Pw|=p^{n-a} (***<----EDIT: This line has been changed.***)
2. Pw(0)=0^{n-a}w
3. Pw(.)=(p-1)^{n-a}(w*) (***<----EDIT: This line has been changed.***)
4. Every word in Qn is in exactly one path
where w* is essentially treating the "p-1" digits as "1"s and taking the complement. So again in base 5, if you have w=4044, then w*=0400.

I THINK that this implies the following Lemmas (with proofs similar to those in your paper):

I could have made a mistake, though. And who knows whether these things ever exist; I haven't bothered to check even the simplest cases.

I've put a little thought into larger cubes; a lot of things that are simple for Q_n get much more complicated. In particular, n = 3, a = 0, p = 3 works; you can cover a 3x3x3 cube while with a path from 000 to 222, so your proposed generalized Lemma 1 doesn't hold.

[edit] It's been a while since I worked with this. [/edit]

Last edited by FiddleMath on Wed May 09, 2007 4:20 am UTC, edited 1 time in total.

FiddleMath wrote:I've put a little thought into larger cubes; a lot of things that are simple for Q_n get much more complicated. In particular, n = 3, a = 1, p = 3 works; you can cover a 3x3x3 cube while with a path from 000 to 222, so your proposed generalized Lemma 1 doesn't hold.

I probably misread something, but wouldn't B(3,1,3) need to include p^a=3^1=3 distinct paths, rather than just the one? I'll try to post my "proof" later on if I have time (otherwise it'll have to wait until Thursday or so).

EDIT: Also, my Rule 1 was totally wrong; I wrote 3^n, it should have been p^{n-a}. And Rule 3 had a "2" instead of a "p-1."

EDIT 2: Upon further reflection, I hadn't even considered the obvious fact that there are still only 2^n "true" vertices, so clearly that will influence the structure of the bundle. I'll have to think about whether my generalization even makes sense.

I was an extra in the movie Little Big League when I was like 7, you can see me in the background for about 5 seconds during one scene. Yup. I'ma claim that counts, since that's about as far-fetched as some of the erdos-bacon number entries on the wikipedia site.

SpitValve wrote:Maybe I'm just tired, but I don't think I got the jokes in the last 3 posts.

Mine references anti-drug commercials in the US during the 80s and the one after it refers to the Rifleman's Creed, which is famous from the movie Full Metal Jacket. I assume "colon compliance" means that every paper needs to have a colon in its title to be worth anything. Not sure though.

iw wrote:Mine references anti-drug commercials in the US during the 80s and the one after it refers to the Rifleman's Creed, which is famous from the movie Full Metal Jacket. I assume "colon compliance" means that every paper needs to have a colon in its title to be worth anything. Not sure though.

ic. Well, I was only in the US during the 80s for one day, and didn't watch any ads about drugs, as far as I recall. I haven't watched Full Metal Jacket (don't hurt me), but I kinda get the colon thing. w00t!

I just realized that one of my profs last year had an Erdos number of 2. I had the opportunity to proofread a book he was writing (and be credited in the published version for as much), but I didn't do it! Curses! I don't know how close I'll get to a 3 again.